Problems in causal inference can be fruitfully addressed using signal processing techniques. As an example, it is crucial to successfully quantify the causal effects of an intervention to determine whether the intervention achieved desired outcomes. We present a new geometric signal processing approach to classical synthetic control called ellipsoidal optimal recovery (EOpR), for estimating the unobservable outcome of a treatment unit. EOpR provides policy evaluators with both worst-case and typical outcomes to help in decision making. It is an approximation-theoretic technique that relates to the theory of principal components, which recovers unknown observations given a learned signal class and a set of known observations. We show EOpR can improve pre-treatment fit and mitigate bias of the post-treatment estimate relative to other methods in causal inference. Beyond recovery of the unit of interest, an advantage of EOpR is that it produces worst-case limits over the estimates produced. We assess our approach on artificially-generated data, on datasets commonly used in the econometrics literature, and in the context of the COVID-19 pandemic, showing better performance than baseline techniques

翻译：因果推断中的问题可以通过信号处理技术得到有效解决。例如，成功量化干预的因果效应以判断干预是否达到预期结果至关重要。我们提出了一种新的几何信号处理方法，称为椭球最优恢复（EOpR），用于经典合成控制中估算处理单元不可观测的结果。EOpR为政策评估者提供最坏情况和典型情况下的结果，以辅助决策。这是一种近似理论技术，与主成分分析理论相关，能够在给定学习信号类别和一组已知观测值的情况下恢复未知观测值。我们证明，与因果推断中的其他方法相比，EOpR可以改善处理前的拟合效果并减少处理后的估计偏差。除了恢复目标单元外，EOpR的一个优势是它能产生估计值的上界下限。我们在人工生成数据、计量经济学文献常用数据集以及COVID-19疫情背景下评估了该方法，显示出优于基线技术的性能。